Q 4(a) [5 Marks] A vendor has the probability of 70% for a favourable market and...

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Q 4(a) [5 Marks] A vendor has the probability of 70% for a favourable market and the probability of 30% for an unfavourable market. The payoff matrix for his/her actions is given below: Decision Large plant Small plant States of Nature Favourable Mkt Unfavourable Mkt P=70% P=50% 200,000 100,000 0 -180,000 -20,000 0 No plant Calculate the Expected Monetary Value from each action and then recommend an appropriate action for the vendor. Q 4(b) [11 Marks] A distributor buys perishable goods for 2 per item and sells them at 5. Demand per day is uncertain; items unsold at the end of the day represent a write-off because of perishability. If distributor understocks, then he/she loses profit that could have been made. A 300-day record of past activity is as follows: Daily demand (units) No. of days P(probability) 10 30 0.1 (=30/300) 11 60 0.2 (=60/300) 12 120 0.4 (=120/300) 13 90 0.3 (=90/300) (Column sums) 300 1 Calculate the Conditional and Expected Profits. What level of stock should be held from day to day to maximise profit? Q 4(c) [9 Marks] The following economic conditions can be seen for 3 differing types of investment in the table below: Economic Conditions (states) Investment High Growth Moderate Growth Low Growth Shares 10000 6500 -4000 Bonds 8000 6000 1000 Savings 5000 5000 5000 CA3000 - Quantitive Analysis for Business Decisions Semester 1 Examinations 2022/2023 Page 4 of 9 Calculate the following criterion and indicate the recommended selection for each one: i. Laplace ii. Maximin - Best of the worst iii. Maximax - Best of the best (3 marks) (3 marks) (3 marks) Q 4(a) [5 Marks] A vendor has the probability of 70% for a favourable market and the probability of 30% for an unfavourable market. The payoff matrix for his/her actions is given below: Decision Large plant Small plant States of Nature Favourable Mkt Unfavourable Mkt P=70% P=50% 200,000 100,000 0 -180,000 -20,000 0 No plant Calculate the Expected Monetary Value from each action and then recommend an appropriate action for the vendor. Q 4(b) [11 Marks] A distributor buys perishable goods for 2 per item and sells them at 5. Demand per day is uncertain; items unsold at the end of the day represent a write-off because of perishability. If distributor understocks, then he/she loses profit that could have been made. A 300-day record of past activity is as follows: Daily demand (units) No. of days P(probability) 10 30 0.1 (=30/300) 11 60 0.2 (=60/300) 12 120 0.4 (=120/300) 13 90 0.3 (=90/300) (Column sums) 300 1 Calculate the Conditional and Expected Profits. What level of stock should be held from day to day to maximise profit? Q 4(c) [9 Marks] The following economic conditions can be seen for 3 differing types of investment in the table below: Economic Conditions (states) Investment High Growth Moderate Growth Low Growth Shares 10000 6500 -4000 Bonds 8000 6000 1000 Savings 5000 5000 5000 CA3000 - Quantitive Analysis for Business Decisions Semester 1 Examinations 2022/2023 Page 4 of 9 Calculate the following criterion and indicate the recommended selection for each one: i. Laplace ii. Maximin - Best of the worst iii. Maximax - Best of the best (3 marks) (3 marks) (3 marks)